Studying Black Holes in Superposition Using Unruh-DeWitt Particle Detectors

Abstract

In quantum gravity, we expect black holes to exist in quantum superposition. However, the measurable effects of black hole superpositions have not been studied widely. In this thesis, we study superpositions of different periodically identified Minkowski spacetimes and different Banados-Teitelboim- Zanelli (BTZ) black hole spacetimes and investigate excited state probabilities of an Unruh-DeWitt particle detector coupling to the superposition of these spacetimes. This thesis is based on two consequent articles on the phenomenology of quantum superpositions of spacetime. The primary research focus is to superpose the mass of the Banados-Teitelboim-Zanelli (BTZ) black hole and investigate the quantum-gravitational effects produced by such a spacetime. We start by investigating a cylindrical spacetime superposition to better understand the basic framework for superposing spacetimes and the corresponding effects induced on the quantum matter. We achieve this by superposing a periodically identified Minkowski spacetime (i.e. Minkowski spacetime with a periodic boundary condition that creates a cylindrical topology), for which we develop an operational approach for constructing spacetime superpositions using the notion of nonlocal correlations and automorphic fields in curved spacetime. We then use this method to superpose a black hole of different masses for the nonrotating BTZ spacetime. Following that, we couple quantum matter (which we model using the Unruh-DeWitt (UDW) particle detector model) to these spacetime superpositions. Firstly, we couple it to the cylindrical spacetime to demonstrate for the first time the response of a UDW detector to a scalar field in this superposed spacetime, and its dependence on the energy gap Ω, and γ = lA/lB, where lA and lB are the characteristic lengths of the periodically identified Minkowski spacetimes in superposition. The detector’s response exhibits quantum-gravitational “resonances” at rational ratios of the superposed periodic length scale. Secondly, we couple a UDW particle detector to a scalar quantum field in the spacetime produced by a mass-superposition of the BTZ black hole. We show that the detector’s dynamics exhibit similar resonances to the Minkowski spacetime superposition, now manifesting at rational ratios of the square root of the superposed black hole mass. Such resonances are genuinely quantum-gravitational effects arising from the black hole mass superposition that support and extend Bekenstein’s original conjecture concerning the quantization of black holes in quantum gravity.